Sloane Stephens gets text messages from grandpa

Sloane Stephens of the United States serves to Kristina Mladenovic of France during their second round match at the Australian Open tennis championship in Melbourne, Australia, Thursday, Jan. 17, 2013. (AP Photo/Andy Wong)
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Sloane Stephens of the United States serves to Kristina Mladenovic of France during their second round match at the Australian Open tennis championship in Melbourne, Australia, Thursday, Jan. 17, 2013. (AP Photo/Andy Wong)
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Perspiration drips down the face of Australia's James Duckworth after his second round loss to Slovenia's Blaz Kavcic at the Australian Open tennis championship in Melbourne, Australia, Thursday, Jan. 17, 2013. (AP Photo/Andy Wong)— AP

Perspiration drips down the face of Australia's James Duckworth after his second round loss to Slovenia's Blaz Kavcic at the Australian Open tennis championship in Melbourne, Australia, Thursday, Jan. 17, 2013. (AP Photo/Andy Wong)
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Slovenia's Blaz Kavcic tries to cool off during a break in his second round match against Australia's James Duckworth at the Australian Open tennis championship in Melbourne, Australia, Thursday, Jan. 17, 2013. (AP Photo/Andy Wong)— AP

Slovenia's Blaz Kavcic tries to cool off during a break in his second round match against Australia's James Duckworth at the Australian Open tennis championship in Melbourne, Australia, Thursday, Jan. 17, 2013. (AP Photo/Andy Wong)
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Taiwan's Lu Yen-Hsun hits a backhand return to France's Gael Monfils during their second round match at the Australian Open tennis championship in Melbourne, Australia, Thursday, Jan. 17, 2013. (AP Photo/Rob Griffith)— AP

France's Gael Monfils waves to the crowd following his five set win over Taiwan's Lu Yen-Hsun in their second round match at the Australian Open tennis championship in Melbourne, Australia, Thursday, Jan. 17, 2013. (AP Photo/Rob Griffith)— AP

France's Gael Monfils waves to the crowd following his five set win over Taiwan's Lu Yen-Hsun in their second round match at the Australian Open tennis championship in Melbourne, Australia, Thursday, Jan. 17, 2013. (AP Photo/Rob Griffith)
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Kristina Mladenovic of France hits a return to Sloane Stephens of the United States during their second round match at the Australian Open tennis championship in Melbourne, Australia, Thursday, Jan. 17, 2013. (AP Photo/Andy Wong)— AP

Kristina Mladenovic of France hits a return to Sloane Stephens of the United States during their second round match at the Australian Open tennis championship in Melbourne, Australia, Thursday, Jan. 17, 2013. (AP Photo/Andy Wong)
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Sloane Stephens of the United States rests in the the shade, near a ball boy, during her second round match against Kristina Mladenovic of France at the Australian Open tennis championship in Melbourne, Australia, Thursday, Jan. 17, 2013. (AP Photo/Andy Wong)— AP

Sloane Stephens of the United States rests in the the shade, near a ball boy, during her second round match against Kristina Mladenovic of France at the Australian Open tennis championship in Melbourne, Australia, Thursday, Jan. 17, 2013. (AP Photo/Andy Wong)
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Sloane Stephens of the United States hits a return to Kristina Mladenovic of France during their second round match at the Australian Open tennis championship in Melbourne, Australia, Thursday, Jan. 17, 2013. (AP Photo/Andy Wong)— AP

Sloane Stephens of the United States hits a return to Kristina Mladenovic of France during their second round match at the Australian Open tennis championship in Melbourne, Australia, Thursday, Jan. 17, 2013. (AP Photo/Andy Wong)
/ AP

MELBOURNE, Australia 
One of the things Sloane Stephens likes about winning at the Australian Open is that her tech-savvy grandparents can keep watching her from back home.

"My grandpa texted me," the 19-year-old Stephens said. "He said they stayed up again to watch me `on the machine' as my grandpa calls it."

That's the computer.

Grandpa got to see Stephens advance Thursday to the third round, beating France's Kristina Mladenovic 6-4, 6-3. It's one of many reasons to be proud of her.

Stephens is the No. 3-ranked American woman and has climbed to a career high world ranking of No. 25. Her ascent has been quick after ending 2012 ranked 38th, which made her the youngest player inside the year-end top 50.

Last year, Stephens was one of the up-and-coming players to watch. She reached the third round at Wimbledon and the U.S. Open and the fourth round at the French Open. She has achieved her best result in Melbourne after exiting in the second round at last year's Australian Open.

For Stephens, Thursday's match was personal.

She has played the 19 -year-old Mladenovic on big stages before, namely the semifinals of the 2009 French Open juniors tournament, where she lost.

Asked if she remembered that match, Stephens replied: "How could I forget?"

"That match made my career. I was devastated," said Stephens, who is bubbly and charmingly confident. "I cried for like a month after that.

"But if we had never played before, it would have been super difficult to get out there and play now, so I think that kind of helped."

By her accounting, Stephens "didn't play that great" on Thursday. The 98th-ranked Mladenovic was hitting big serves and big forehands and Stephens had trouble finding her rhythm. She felt her mind wander but then she steered it back to the game.

When asked how she pulled herself out of tight spots, Stephens talked more about her mindset than her tennis.

"I think it's a mixture of things. Concentration, confidence, willing to run every ball down," she said. "Today I was determined to get the next ball back."

Staying focused leads to other rewards, she smiled.

Like a pair of Jimmy Choos.

Before coming to Melbourne, Stephens had promised herself: "If I stay focused and concentrate, then I'll reward myself with Jimmy Choo shoes."

How much will those shoes set her back?

"You don't want to know," she said with big eyes. "It's like five meals. And I eat a lot."

Stephens' next opponent is Laura Robson, a British teenager she has known since she was 12.